Estevez–Mansfield–Clarkson equation

The Estevez–Mansfield–Clarkson equation is a nonlinear partial differential equation introduced by Pilar Estevez, Elizabeth Mansfield, and Peter Clarkson.[1]

If U is a function of some other variables x, y, t, then we denote ${\displaystyle {\frac {\partial ^{3}U}{\partial t\,\partial y^{2}}}}$ by U_tyy, and so on. With that notation, the equation is

${\displaystyle U_{tyyy}+\beta U_{y}U_{yt}+\beta U_{yy}U_{t}+U_{tt}=0}$

in which ${\displaystyle U=u(x,y,t).}$

References

1. Li Zhibing Traveling Wave Solution of Nonlinear Mathematical Physics equations SCIENCEP 2008(李志斌编著 《非线性数学物理方程的行波解》 页 科学出版社 2008)

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